If you compare the Shannon index to the classical definition of entropy, you can find that the ratio of the two is Boltzman's constant. This means, that if you could calculate all of the Shannon index entropy on Earth, and divided it by all of the entropy in the universe, and it did NOT come out to Boltzman's constant, that life must exist somewhere else in the universe.
Update 19.12.2010:
I now believe this statement to be false. Actually, there is no distinction between living and non-living chemical entities, just a gradient of complexity. Based on the work of Libb Thims, the human molecule has already been defined. Boltzman's constant is probably a sort of non-linear reaction rate which describes the current location in time since the big bang w.r.t. (the Earth's?) chemical evolutionary process.
Update 11.01.2011:
The statement of belief of Boltzmann's constant needs to be corrected as well. It is a relic of the unfortunate use of unitless degrees in describing temperature, instead of giving it units of energy. Thus Boltzmann's constant should be used to describe the quantity of energy kT, instead of T.